Khan.scratchpad.disable(); For every level Vanessa completes in her favorite game, she earns $560$ points. Vanessa already has $270$ points in the game and wants to end up with at least $2270$ points before she goes to bed. What is the minimum number of complete levels that Vanessa needs to complete to reach her goal?
Explanation: To solve this, let's set up an expression to show how many points Vanessa will have after each level. Number of points $=$ $ $ Levels completed $\times$ Points per level $+$ Starting points Since Vanessa wants to have at least $2270$ points before going to bed, we can set up an inequality. Number of points $\geq 2270$ Levels completed $\times$ Points per level $+$ Starting points $\geq 2270$ We are solving for the number of levels to be completed, so let the number of levels be represented by the variable $x$ We can now plug in: $x \cdot 560 + 270 \geq 2270$ $ x \cdot 560 \geq 2270 - 270 $ $ x \cdot 560 \geq 2000 $ $x \geq \dfrac{2000}{560} \approx 3.57$ Since Vanessa won't get points unless she completes the entire level, we round $3.57$ up to $4$ Vanessa must complete at least 4 levels.